On adaptive control of stochastic bilinear systems

The minimum variance control law for bilinear systems with known parameters is shown to yield in most cases controls with infinite variance; this calls into question the use of the so-called bilinear self-tuning regulators. An adaptive weighted minimum variance controller based upon the cost with weighted control efforts is suggested for first-order bilinear systems and is shown to yield boundedness of the closed-loop system variables under a certain condition on the parameter estimate.